Abstract
This method is based on the generalized Taylor's series formula together with the residual error function. The basic concept of residual power series method (RPSM) and related theorems are first discussed in this chapter. Further, this method is used to address two problems, viz. linear fractional one-dimensional heat-like equation and nonlinear fractional advection equation. The results obtained by the present method reveal the accuracy and fast convergence of the present method. Usually, the series converges with an increase in terms, but again the compact form of solution cannot always be expected.
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